New York has recently posted sets of sample questions for grades 3 through 8 that are designed to help teachers think about the instructional shifts that will be needed as we move to the Common Core State Standards for for both ELA and Math
http://www.p12.nysed.gov/apda/common-core-sample-questions/
* Multiple Choice
* Short Constructed Response
* Extended Constructed Response
As you look at these sample questions, the New York site recommends you do the following:
* Interpret the way the standards are conceptualized in each question.
* Note the multiple ways the standard is assessed throughout the sample questions.
* Take note of numbers (e.g., fractions instead of whole numbers) used in the samples.
* Pay attention to the strong distractors in each multiple-choice question.
* Don’t consider these questions to be the only way the standard will be assessed.
* Don’t assume that the sample questions represent a mini-version of future state assessments.
I've selected a few samples from each grade level that seemed particularly noteworthy.
3rd Grade
4th Grade Fractions -- a challenging multi-step problem.. Many students would benefit from knowing how to use bar diagrams to help conceptualize this problem. To learn more about bar diagrams, take a look at
www.thinkingblocks.com.
4th Grade Operations and Algebraic Thinking -- this problem requires students to move beyond step-by-step arithmetic thinking. They'll need to have lots of experiences "telling the story from beginning to end" using numbers and symbols.
5th Grade Number and Operations in Base Ten -- this is a very different kind of place value question than most textbooks currently ask. Instead of asking the value of the 5, they're asking for a relative comparison that involves a clear understanding that every place value is 10 times larger than the place value to its immediate right.
5th Grade Number and Operations: Fractions -- Students will need experiencing creating their own fraction models and also understanding what is meant by "expression". From examples in the Progressions fraction document, it seems clear that rectangular area models will be an important tool for students, along with some experience with circle area models. Also, we will all need to make sure we understand the difference between a "visual model" and "mathematical modeling".
5th Grade Measurement -- another multi-step word problem, with the additional challenges of metric conversion with decimal quantities. A nice approach to metric conversions can be found in the Primary Math materials from Singapore, where students learn to think of 5.6 meters as 5 meters and 60 centimeters, which can then be more easily converted to 500 cm + 60 cm. After working with undergraduates who have only learned to convert using the King Henry ... mnemonic, I would highly recommend moving away from this procedure without understanding to something more like what Singapore has students understand.
6th Grade Expressions and Equations -- This evaluation of a 4-term expression with exponents above 2 might more typically have been seen in 7th and 8th grades. This would indicate that 6th grade teachers will want to add algebra tiles to their teaching repertoire. Notice also that there is much more room for student error in this constructed response format, so having students develop the habit of mind of double checking their work (Accuracy and Precision Math Standard) will be important.
6th Grade Measurement and Expressions/Equations -- Another question that anticipates that students will be able to add like terms, and use the distributive property with algebraic expressions. It also challenges students to understand that when linear measures are scaled (such as perimeter) the scale factor remains the same, but when area measures are scaled, the scale factor is squared. In this problem, though, students can use calculations in Part C if they are unsure of this high-level understanding.
6th Grade Geometry -- This is a multi-step geometry problem on a coordinate plane. Notice that students will need experience with coordinate axes where the interval is greater than 1. Many textbooks provide primarily single-step problems in geometry, where students are either asked to plot points, or identify a triangle on the coordinate plane, or find the area of a triangle or other quadrilateral -- but not all of these at one time.
7th Grade Sample Questions -- note the incorporation of fractions and mixed numbers that increase the complexity of the items.
8th Grade Sample Questions -- note the expectation that students will be able to "explain" and "justify" in their constructed response questions. Also, the questions about slope will require students to have a strong conceptual understanding of slope, and to be able to move comfortably between the concept of slope as seen in tables, graphs, and equations.
These are some of my observations after a first look at the New York Sample Questions. Once you've had a chance to look at the items, it would be great to get your additional observations -- feel free to add your comments to this post.
Thanks for all that you do for students!
